Abstract

Many brain morphometry studies have been performed in order to characterize the brain atrophy pattern of Alzheimer's disease (AD). The earliest studies focused on the volume of particular brain structures, such as hippocampus and entorhinal cortex. Even though volumetry is a powerful, robust and intuitive technique that has yielded a wealth of findings, more complex shape descriptors have been used to perform statistical shape analysis of particular brain structures. However, in shape analysis studies of brain structures the information of the relative pose between neighbor structures is typically disregarded. This work presents a framework to analyse pose information including the following approaches: similarity transformations with either pseudo-Riemannian or left-invariant Riemannian metric, and centered transformations with a bi-invariant Riemannian metric. As an illustration, an analysis of covariance (ANCOVA) and a discrimination analysis were performed on Alzheimer's Disease Neuroimaging Initiative (ADNI) data.

Example of a square object following a trajectory given by: Sim(3) one-parame ter subgroup (top-left); Sim(3) left-invariant geodesic (top-right); centered transformations with center c in the center of the object (bottom-left); and centered transformations with center c at the top-right corner (bottom-right). In bottom panels, the center c is indicated with a dot. A straight dashed-line connecting the top-right corner of the object from initial to end pose is shown for comparison purposes.